# Combination formula for 3 numbers

How to write the combination formula $$x \choose y$$ for 3 numbers? This is my problem:

We have a die with these sides (1,1,1,1,2,3), all sides are equiprobable. We are rolling 10 times. What is the probability of having 6*1, 3*2 and 1*3?

• You mean $6$ times $1$ , $3$ times $2$ and once $3$ ? – Peter Mar 10 at 16:53
• – kimchi lover Mar 10 at 16:54
• @Peter yes, that’s what I mean – Tigran Minasyan Mar 10 at 16:56

$$\displaystyle{n \choose k_1, k_2, \ldots, k_m} = \frac{n!}{k_1!\, k_2! \cdots k_m!}$$
In your case it is $$m=3, k_1=6,k_2=3, k_3=1$$
$$\displaystyle{10 \choose 6, 3, 1}$$